Consider the Statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$

question 1

Essay

Consider the statement $$\text { For all sets } A \text { and } B , ( A - B ) \cap B = \emptyset \text {. }$$
Complete the proof begun below in which the given statement is derived algebraically from
the properties listed in Theorem 6.2.2. Be sure to give a reason for every step that exactly justifies what was done in the step: Proof:
Let $A$ and $B$ be any sets. Then the left-hand side of the equation to be shown is

which is the right-hand side of the equation to be shown. [Hence the given statement is true.]
(The number of lines in the outline shown above works for one version of a proof. If you write
a proof using more or fewer lines, be sure to follow the given format, supplying a reason for
every step that exactly justifies what was done in the step.)

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Definitions:

Extinction Process

In behavioral therapy, the gradual weakening of a conditioned response by discontinuing reinforcement for it.

Symptom Stimuli

Triggers or cues that can precipitate or exacerbate symptoms of a psychological or physical disorder.

Psychopathology

The scientific study of mental disorders, including their symptoms, causes, and treatments.

Emotional Reactivity

The extent to which an individual responds emotionally to situations, indicating how sensitive they are to environmental stimuli.